Mathematical Modeling of Schistosomiasis Transmission Using Reaction-Diffusion Equations

Abstract

Schistosomiasis, a neglected tropical disease caused by parasitic trematodes of the genus \textit{Schistosoma}, affects millions of people in tropical and subtropical regions lacking access to clean water and proper hygiene. With its impact on health and well-being, the World Health Organization aspires to eliminate schistosomiasis by 2030. This work addresses the challenge of effective control in endemic areas by integrating diffusion in each sub-population using reaction-diffusion equations. The proposed model includes treated individuals who have undergone massive drug administration and a time-dependent function that models the change in human behavior. We present a Partial Differential Equation (PDE) model of schistosomiasis spread that incorporates population movement and human behavior change. Mathematical analysis explores the system's dynamics according to the infection threshold $R_0$, shedding light on the disease's behavior. Sensitivity analysis is used to identify the key parameters affecting disease spread. Numerical simulations under different scenarios elucidate the impact of human behavior on disease dynamics. This research contributes to a deeper understanding of schistosomiasis transmission and provides insights into control strategies.